Effects of bursty traffic in service differentiated Optical Packet Switched networks

Transcription

1 Effects of bursty traffc n servce dfferentated Optcal Packet Swtched networks Harald Øverby, orvald Stol Department of Telematcs, orwegan Unversty of Scence and Technology, O.S. Bragstadsplass E, -749 Trondhem, orway haraldov@tem.ntnu.no Abstract: Servce dfferentaton s a crucal ssue n the next -generaton Optcal Packet Swtched networks. In ths paper we examne how bursty traffc nfluences the performance of a servce dfferentated Optcal Packet Swtched network. By usng tme -contnuous Markov chans, we derve explct results for the packet loss rates n the case of a bursty hyperexponental arrval process. Results ndcate that the performance s degraded as the burstness of the arrval process ncreases. 4 Optcal Socety of Amerca OCIS codes: (6.45) etworks; (6.45) Optcal Communcatons References and lnks. M. O Mahony, D. Smeondou, D. Hunter and A. Tzanakak, The Applcaton of Optcal Packet Swtchng n Future Communcaton etworks, IEEE Communcatons Magazne 39, 8-35 ().. X. Xao and L. M., Internet QoS: A Bg Pcture, IEEE etwork 3, 8-8 (999). 3. B. Wydrowsk and M. Zukerman, QoS n Best -Effort etworks, IEEE Communcatons Magazne 4, (). 4. M. Yoo, C. Qao and S. Dxt, QoS Performance of Optcal Burst Swtchng n IP -Over-WDM etworks, IEEE Journal on Selected Areas n Communcatons 8, 6-7 (). 5. H. Øverby and. Stol, A Teletraffc Model for Servce Dfferentaton n OPS networks, n Proceedngs of IEEE 8th Optoelectroncs and Communcatons Conference (Insttute of Electrcal and Electronc Engneers, 3), pp Ayman Kaheel, Tamer Khattab, Amr Mohamed and Hussen Alnuwer, Qualty-of-Servce Mechansms n IP-over WDM etworks, IEEE Communcatons Magazne 4, (). 7. W. Leland, M. Taqqu, W. Wllnger and D. Wlson, On the Self Smlar ature of Ethernet Traffc (Extended Verson), IEEE/ACM Transactons on etworkng, -5 (994). 8. A.L. Schmd et al., Impact of VC mergng on buffer requrements n ATM networks, Proceedngs of Eghth Internatonal Conference on Hgh Performance etworkng, 3-7 (998). 9. Deepankar Medh, Some Results for Renewal Arrval to a Communcaton Lnk, Probablty Models and Statstcs: A J. Medh Festschrft, 85-7 (996).. S. Bjørnstad,. Stol and D. R. Hjelme, Qualty of servce n optcal packet swtched DWDM transport networks, n Asa -Pacfc Optcal and Wreless Communcatons Conference, Proc. SPIE 49, ().. E. V. Breusegem, J. Cheyns, B. Lannoo, A. Ackaert, M. Pckavet and P. Demeester, Implcatons of usng offsets n all-optcal packet swtched networks, n Proceedngs of IEEE Optcal etwork Desgn and Modellng (Insttute of Electrcal and Electronc Engneers, ).. Leonard Klenrock, Queueng Systems Volume I: Theory (John Wley & Sons, 975).. Introducton In order to ncrease avalable capacty n future core networks, Wavelength Dvson Multplexng (WDM) has emerged as a vable technology []. Among the dfferent WDM swtchng technologes proposed n recent lterature, Optcal Packet Swtchng (OPS) has emerged as the most promsng, at least n the long run, due to the benefts from statstcal multplexng and adaptablty to changes n the network nfrastructure and traffc pattern []. Today s Internet provdes only the best-effort servce, where each packet s gettng the same treatment and there are no guarantees to the end-to-end delay or the packet loss rate #357 - $5. US Receved December 3; revsed 3 January 4; accepted 3 January 4 (C) 4 OSA 9 February 4 / Vol., o. 3 / OPTICS EXPRESS 4

2 (PLR) []. However, the ncreasng number of real-tme applcatons and nteractve Internet applcatons demand a strcter Qualty of Servce (QoS) than the current best-effort servce can offer. Although the best-effort servce s not suted to carry real-tme or nteractve applcatons, t s well suted for web browsng, e-mal and other relaxed servces. Hence, n order to gve dfferent applcatons ther needed level of QoS and to utlze network resources optmally, servce dfferentaton should be present n future core networks []. Exstng servce dfferentaton schemes for tradtonal store-and-forward networks mandate the use of electronc buffers to solate the dfferent traffc classes,.e. by the use of actve queue management algorthms [3]. Here, all packet arrvals to a swtch are stored n the buffer and managed accordng to an actve queue management algorthm, whch solate the dfferent servce classes by markng, droppng or reorderng packets n the queue [3]. However, as ponted out n [4], such schemes are not sutable for the WDM layer. Frst, electronc bufferng necesstates the use of optcal-electrcal converters, whch results nn a sgnfcant ncrease n the cost of the swtch. Second, although optcal bufferng can be realzed by utlzng Fbre Delay Lnes (FDLs), they can only gve lmted bufferng capabltes compared to electronc bufferng, because data s delayed by traversng a fxed length optcal fbre (.e. the FDL s not a Random Access Memory). Hence, performng actve queue management on FDL buffers s not an easy task, as complex management s requred. Also, usng FDLs makes the swtches bulky and costly, especally when large amounts of data need to be buffered. Hence, as ponted out n [4], a vable servce dfferentaton scheme for future optcal core networks s to utlze bufferless methods to solate the dfferent servce classes. One such bufferless method s the Wavelength Allocaton algorthm (WA) [5,6]. Accordng to [7], the Internet traffc shows a self-smlar pattern, whch means that the traffc s equally bursty when vewed over dfferent tme scales. Regardng arrvals to an optcal swtch, ths results n perods wth many arrvals and perods wth lttle or no arrvals. The wdely used Posson process does not model such traffc very well, whch means that other arrval processes should be consdered, e.g. the hyper-exponental arrval process [8,9]. In earler works we have presented an analytcal model of the WA n the case of a nonbursty Posson arrval process [5]. Ths paper presents an analytcal model of the WA n the case of a bursty hyper-exponental arrval process and further consders the mpacts of bursty traffc on the network performance. The rest of the paper s organzed as follows. Secton presents the system model. Secton 3 presents the WA, accompaned by analytcal models. Secton 4 presents smulaton and analytcal results, whle Secton 5 concludes the paper.. System model We consder a network wth two servce classes, where servce class s gven hgher prorty than servce class (the use of two servce classes only n the core networks s argued by the authors of []). Snce the swtches n the network have no buffers for contenton resoluton, the aggregated delay wll be very small compared to the delay from the access network, and can thus be gnored []. However, a major concern s such networks s packet losses, whch s caused by external blockng (.e. contentons at an output port). Hence, n ths paper we focus on the PLR as the sole QoS parameter, whch means that the dfferent servce classes wll be solated from each other based on dfferent PLRs. When a packet arrves at the swtch, the packet header s extracted and processed electroncally by the control module. Whle the header s processed, the packet payload s buffered usng FDL processng buffers (as seen n Fg. (a) []. Based on the destnaton nformaton extracted from the packet header, the control module decdes whch output fbre the packet s swtched to and confgures the swtch fabrc accordngly. For the rest of the paper we focus on a sngle optcal core swtch and assume the followng: The optcal swtch operates n asynchronous mode. The swtch utlzes full wavelength converson. The swtch has F nput- and output fbres, as shown n Fg. (a). #357 - $5. US Receved December 3; revsed 3 January 4; accepted 3 January 4 (C) 4 OSA 9 February 4 / Vol., o. 3 / OPTICS EXPRESS 4

3 By utlzng WDM, each fbre provdes wavelengths (channels) to transport data, each wavelength wth a specfed capacty C bps. We assume a unform traffc pattern, whch means that we have an equal load on every output fbre and can restrct our study to consder the PLR on a sngle output fbre, marked red n Fg. (a). Packets arrve to the output fbre accordng to ether a Posson process (see Secton 3.) or a -stage hyper-exponental process. The hyper-exponental arrval process s depcted n Fg. (b) and wll be dscussed n Secton 3.. The relatve share of class traffc s S, whle the relatve share of class traffc s S. The packet lengths for both class and class traffc are exponental ndependent dentcal dstrbuted (..d.) wth mean servce tme µ -. A l m, where λ s the offered traffc ntensty. The system load s defned as ( ) The effects of the swtchng tme are gnored. Control Module a θ S S ϕ, S θ ϕ, S θ S F -a θ S ϕ, S θ ϕ, S θ a b Fg.. An optcal packet swtch (a) and the -stage hyper-exponental arrval process wth prortes (b). 3. The Wavelength Allocaton algorthm (WA) In order to solate the two servce classes, we utlze the WA. In the WA, a total of avalable wavelengths at the output fbre are dvded nto two pools accordng to prorty,.e. a class pool wth W wavelengths and a class pool wth W wavelengths [6]. Incomng packets to the output fbre can access these wavelengths only f they have the necessary prorty level. Ths means that class traffc can access wavelengths only from the class pool (total of n W wavelengths), whle class traffc can access wavelengths from both pools (total W + W wavelengths). Incomng packets whch fals to acqure a wavelength s mmedately dropped at the node. By adjustng the varable n, we acheve any desred level of the PLR for class traffc. 3. Posson arrval process In the case of Posson arrval process, the output fbre s modeled accordng to a modfed M/M// queung model. Explct results for the PLRs have been derved n earler works (see [5]), and wll not be detaled any further n ths paper. 3. Two-stage hyper-exponental arrval process We now turn our attenton to a -stage hyper-exponental (H ) arrval process wth parameters a, θ and θ, as seen n Fg. (b) [8]. Due to the memory-less property of the exponental #357 - $5. US Receved December 3; revsed 3 January 4; accepted 3 January 4 (C) 4 OSA 9 February 4 / Vol., o. 3 / OPTICS EXPRESS 4

4 dstrbuton, the H arrval process s not long range dependent, but stll bursty. We see from Fg. (b) that there s a probablty a that the ntensty of the next nter-arrval tme s θ (marked red) and a probablty -a that the ntensty of the next nter-arrval tme s θ (marked dotted red). We denote these arrvals as type and type arrvals, respectvely. Furthermore, regardless of the arrval type, we see that the probablty for a class (blue) and class (green) arrval s S and S, respectvely. Hence, the ntensty of a type k arrval wth prorty l ( kl,, ) s ϕ l,k. We also see that q j, + j, (,). The burstness of ths process can be characterzed accordng to the squared coeffcent of varaton, gven as [9,]: c æ s ö m a + k - ak ç e çèm ø m a+ k- a k ( ) Here, m s the th moment of the H process, σ s the varance, ε s Palms form factor [] andk q q. ϕ, a ϕ, a θ a () µ (n-)µ nµ (n+)µ (-)µ µ P P n- P n P - θ a θ a θ a ϕ, a ϕ, a ϕ, a P θ (-a) θ a θ a θ (-a) θ (-a) θ a ϕ, (-a) ϕ, a ϕ, (-a) ϕ, a ϕ, a ϕ, (-a) ϕ, (-a) ϕ, a ϕ, a ϕ, (-a) θ (-a) θ a R µ (n-)µ nµ (n+)µ (-)µ µ R n- R n R - θ (-a) θ (-a) θ (-a) ϕ, (-a) ϕ, (-a) ϕ, (-a) R ϕ, (-a) ϕ, (-a) θ (-a) Fg.. Tme contnuous Markov chan of the WA wth H -arrval process. Fgure shows a tme-contnuous Markov chan of the WA wth H -arrval process. The states P and R ( ) denote the number of packets currently n transmsson at the output fbre, e.g. n state P, packets are currently n transmsson. We defne p and r as the state probabltes for beng n state P and R, respectvely. In the P states (not dotted), the next arrval s a type arrval, whle n the R states (dotted) the next arrval s a type arrval. Furthermore, regardless of state, we see from Fg. that the probablty to end n state P ( ) equals a,.e. the probablty that the next arrval s a type arrval. On the opposte, the probablty to end up n state R ( ) s -a, whch s n accordance wth the model n Fg. (b). Furthermore, n the blue and black states, only class traffc s accepted. Hence, n the case of a class arrval, the number of packets currently n transmsson does not change, although the arrval type of the next arrval may change. In the black states, both class and class traffc s dscarded. From Fg. we can easly derve the node equatons as follows: p q p m, r q r m () p ( m+ q) a ( p- q+ r- q) + p+ ( + ) m n- (3) ( ) ( ) ( ) p n m+ q a p q + p j + r q + r j + p n+ m (4) n n- n, n- n, n+ #357 - $5. US Receved December 3; revsed 3 January 4; accepted 3 January 4 (C) 4 OSA 9 February 4 / Vol., o. 3 / OPTICS EXPRESS 43

5 ( m+ q) ( - j, + j,+ - j,+ j,) p a p p r r + ( ) + p + m ( ) -, -, n+ - p q a p j + p q + r j + r q (6) r ( m q) ( a) ( r- q p- q) r+ ( ) m n ( ) ( ) ( -, -,) + ( ) ( m q) ( ) ( - j, j, - j, j,) + r + ( + ) m r q ( a) ( r j r q p j p q ) (7) r n m+ q - a r q + r j + p q + r j + r n+ m (8) n n n n n n r + - a r + r + p + p -, -, n () å + å () p r The PLR for class traffc equals the number of lost class arrvals dvded by the total number of class arrvals. We know that class arrvals are dscarded only n states P and R (black states). In state P the arrval ntensty for class traffc s ϕ,, whle n state R the arrval ntensty s ϕ,. Class traffc s lost n the states {P n,,p } and {R n,,r } (blue and black states). Ths leads us to the PLR for class ( P ) and class ( P ) traffc n Eq. (). At last, the average PLR s gven n Eq. (3). p j,+ r j j, H j, å p + j, r å,, p + j, r n n PH j, å p + j, r å - - p q + r q av + j, å p + j, r n å n PH q å p + q r å P 4. Results For the rest of the paper, unless stated dfferently, we have used 4 wavelengths, C,5 Gbps, A,4, S, and n 3. The mean packet length equals 47 bytes, whch means that the mean duraton of a packet s µ -,54 µs. Several smulaton runs have been performed untl the desred level of confdence has been acheved. Frst, smulatons have been performed n order to verfy the analytcal model presented n Secton 3.. Regardng the arrval process, we have used a, and θ 5θ. The results can be seen n Table. H å Table. Smulaton and analytcal results. System load,,4,6,8, H å Analytcal class 6,559-3,379-4,783-7,499 -,3 - Smulaton class 6,45-3,376-4,793-7,476 -,3-95% conf. lmts ±,43-4 ±,636-4 ±,6-4 ±,77-4 ±,63-4 Analytcal class 8,737 -,54-3,374-4,394-5,7 - Smulaton class 8,77 -,54-3,374-4,393-5,7-95% conf. lmts ±,45-4 ±,663-4 ±,544-4 ±,83-4 ±,739-4 From Table we see that the smulaton results matches the analytcal results closely, whch means that the proposed analytcal model s very accurate. Ths s an mprovement compared (5) (9) () (3) #357 - $5. US Receved December 3; revsed 3 January 4; accepted 3 January 4 (C) 4 OSA 9 February 4 / Vol., o. 3 / OPTICS EXPRESS 44

6 to the analytcal models proposed n [9], whch are very naccurate, especally n the case of low system loads. Further n the paper, n order to determne the varables for the H arrval process, we have utlzed the balanced mean ft dstrbuton and the gamma ft dstrbuton [9]. The parameters for the balanced mean ft dstrbuton are seen n Eq. (4), and the parameters for the gamma ft dstrbuton are seen n Eq. (5). æ ö a ( c ) ( c ) ç + - +, q a l, q l ( - a) (4) çè ø ( c ) ( c ) q l æ ç ö çè ø, q 4 l q ( ) ( ) -, ( ) a q q l- q - q (5) PLR,E-3,E-,E-,E+,,4,6,8, System load c^, class c^, class c^ 4, class c^ 4, class c^ 9, class c^ 9, class c^ 6, class c^ 6, class PLR,,,3,4,5, Balanced mean ft Gamma ft c a b Fg. 3. The PLR as a functon of the system load (a) and the average PLR as a functon of the coeffcent of varaton (b). Fgure 3(a) shows the PLR as a functon of the system load for dfferent values of the squared coeffcent of varaton (c ). Here, we have utlzed the balanced mean ft dstrbuton. Frst, regardless of traffc -class, we see that the PLR ncreases when c ncreases. Ths s expected snce an ncrease n c means that the traffc s ncreasngly bursty. Furthermore, we see that the dfference n the PLR decreases as a functon of an ncreasng system load. Ths s because at hgh loads, packet losses are domnated by congeston caused by hgh system load and not bursty traffc. Fgure 3(b) shows the PLR as a functon of the coeffcent of varaton for the balanced mean ft and the gamma ft dstrbuton. Frst, we see that the balanced mean ft dstrbuton show better performance compared to the gamma ft dstrbuton. Second, we see that the ncrease n the PLR decreases when the coeffcent of varaton ncreases, whch means that ncreasng the burstness has greater mpact on the PLR when the arrval process s ntally less bursty. 5. Concluson Ths paper presented an analytcal model of a servce dfferentated bufferless OPS network wth a bursty hyper-exponental arrval process. Although not as general as the models proposed n [9], the proposed model s more accurate, especally at low system loads (.e. A <,8). Results obtaned from the model ndcate that the PLR ncreases as the burstness of the arrval process ncreases, whch s n accordance wth results from prevous research [4,9]. #357 - $5. US Receved December 3; revsed 3 January 4; accepted 3 January 4 (C) 4 OSA 9 February 4 / Vol., o. 3 / OPTICS EXPRESS 45